Binary sdB stars with massive compact companions

SAIt 2008 c

Binary sdB stars with massive compact companions

S. Geier

, C. Karl

, H. Edelmann

, U. Heber

, and R. Napiwotzki

1

Dr. Remeis–Sternwarte, Institute for Astronomy, University Erlangen–Nuremberg, Sternwartstr. 7, 96049 Bamberg, Germany

e-mail: geier@sternwarte.uni-erlangen.de

2

McDonald Observatory, University of Texas at Austin, 1 University Station, C1402, Austin, TX 78712-0259, USA

3

Centre of Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK

Abstract.

The masses of compact objects like white dwarfs, neutron stars and black holes are fundamental to astrophysics, but very difficult to measure. We present the results of an analysis of subluminous B (sdB) stars in close binary systems with unseen compact com- panions to derive their masses and clarify their nature. Radial velocity curves were obtained from time resolved spectroscopy. The atmospheric parameters were determined in a quan- titative spectral analysis. Based on high resolution spectra we were able to measure the projected rotational velocity of the stars with high accuracy. Signs of tidal locking with the companions are visible in the distribution of projected rotational velocities. The detection of ellipsoidal variations in the lightcurve of an sdB binary enabled us to show that subdwarf binaries with orbital periods up to 0.6 d are most likely synchronized. In this case inclina- tion angle and companion mass of the binaries can be tightly constrained. Five invisible companions have masses that are compatible with that of normal white dwarfs or late type main sequence stars. But four sdBs have very massive companions like heavy white dwarfs (> 1 M

), neutron stars or even black holes. Such a high fraction of massive compact com- panions is not expected from current models of binary evolution.

Key words.

binaries: spectroscopic – subdwarfs – stars: rotation

1. Introduction

The mass of a star is its most fundamen- tal parameter. However, a direct measurement is possible in some binary stars only. White dwarfs, neutron stars and stellar black holes are the aftermath of stellar evolution. In bina- ries such faint, compact objects are outshone by their bright companions and therefore their

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orbital motion cannot be measured. As a con- sequence only lower limits to the companion mass can be derived. With the analysis method shown here, these limitations can partly be overcome.

Subluminous B stars (sdBs) are consid-

ered to be helium core burning stars with very

thin hydrogen envelopes and masses around

0.5 M . Different formation channels have

been discussed. As it turned out, a large frac-

tion of the sdB stars are members of short pe- riod binaries (Maxted et al. 2001). For these systems common envelope ejection is the most probable formation channel (Han et al. 2002).

In this scenario two main sequence stars of dif- ferent masses evolve in a binary system. The heavier one will first reach the red giant phase and fill its Roche lobe. If the mass transfer to the companion is dynamically unstable, a com- mon envelope is formed. Due to friction the two stellar cores loose orbital energy, which is deposited within the envelope and leads to a shortening of the binary period. Eventually the common envelope is ejected and a close bi- nary system is formed, which contains a he- lium core burning sdB and a main sequence companion. When the latter reaches the red gi- ant branch, another common envelope phase is possible and can lead to a close binary consist- ing of a white dwarf and an sdB. All known companions of sdBs in such systems are white dwarfs or late type main sequence stars. If mas- sive stars are involved, the primary may evolve into a neutron star (NS) or a black hole (BH) rather than a white dwarf. Since massive stars are very rare, only few sdB+NS or sdB+BH systems are expected to be found.

Since the spectra of the programme stars are single-lined, they reveal no information about the orbital motion of the sdBs’ com- panions, and thus only their mass functions

f

=

comp+M_sdB)²

=

can be calcu- lated. Although the radial velocity (RV) semi- amplitude K and the period P are determined by the RV curve, M

, M

and sin i re- main free parameters. Binary population syn- thesis models (Han et al. 2002) indicate a pos- sible mass range of M

= 0.30−0.48 M for sdBs in binaries, which underwent the com- mon envelope ejection channel. The mass dis- tribution shows a sharp peak at about 0.46 M . This theoretical value could be backed up by observations (e.g. Geier et al. 2007a) as well as by asteroseismology.

For close binary systems, the components’

stellar rotational velocities are considered to be tidally locked to their orbital motions, which means that the orbital period of the system equals the rotational period of the single stars.

If the primary is synchronized in this way the rotational velocity v

=

can be calculated. The stellar radius is given by the mass–radius–relation R =

q

g

. The mea- surement of the projected rotational velocities v

sin i therefore allows us to constrain the systems’ inclination angles i. With M

as free parameter the mass function can be solved and the inclination angle as well as the companion mass can be derived. Because of sin i ≤ 1 a lower limit for the sdB mass is given. To con- strain the system parameters in this way it is necessary to measure K, P, log g and v

sin i with high accuracy.

2. Observations and radial velocity curves

Ten stars were observed at least twice with the high resolution spectrograph UVES at the ESO VLT. Additional observations were made at the ESO NTT (equipped with EMMI), the Calar Alto Observatory 3.5 m telescope (TWIN) and the 4 m WHT (ISIS) at La Palma.

Two of the stars (PG 1232−136, TONS 183) were observed with the high resolution FEROS instrument at the 2.2 m ESO telescope at La Silla. The radial velocities were measured by fitting a set of mathematical functions (Gaussians, Lorentzians and polynoms) to the hydrogen Balmer lines. Sine curves were fit- ted to the RV data points using an χ

minimis- ing method (SVD) and the power spectrum was generated.

3. Atmospheric parameters and projected rotational velocities The spectra were corrected for the mea- sured RV and coadded. Atmospheric parame- ters were determined by fitting simultaneously each observed hydrogen and helium line with a grid of metal-line blanketed LTE model spec- tra. In order to derive v

sin i, we compared the observed spectra with rotationally broad- ened, synthetic line profiles. The latter ones were computed using the LINFOR program.

Since sharp metal lines are much more sensi-

tive to rotational broadening than Balmer or

Fig. 1. Companion mass as a function of primary (sdB) mass of the binaries HE 0532−4503 (left hand panel) and PG 1232−136 (right hand panel). The horizontal line marks the Chandrasekhar limit. The dotted vertical lines mark the theoretical sdB mass range for the common envelope ejection channel (Han et al. 2002).

helium lines, all visible metal lines were in- cluded. A simultaneous fit of elemental abun- dance and projected rotational velocity was performed separately for every identified line using the FITSB2 routine (Napiwotzki et al.

2004). The mean value and the standard devi- ation were calculated from all measurements.

Seeing induced variations in the instrumental profile and the noise level were the dominant error sources. Information on the actual seeing conditions for every exposure have been ex- tracted from the ESO seeing monitor archive.

All other possible sources of systematic errors turned out to be negligible.

4. Nature of the unseen companions Knowing P, K, log g and v

sin i we can calculate the mass of the unseen companion for any given primary mass (see Fig. 1). We adopt the mass range from Han et al. (2002), marked by the dotted lines in Fig. 1. There are no spectral signatures of companions visible.

Main sequence stars with masses higher than 0.45 M could therefore be excluded because they would contribute to the total flux and

could therefore be identified from the spectral energy distribution and/or indicative spectral features. The possible companion masses are given in Tab. 1. Four of the analysed systems have companion masses, which are compati- ble with either typical white dwarfs (WD) or late main sequence stars (late MS). The com- panion of WD 0107−0342 is a massive white dwarf. Since the total mass of the binary may exceed the Chandrasekhar limit, the system is a good candidate for a double degenerate SN Ia progenitor with subdwarf primary, only the second one after KPD 1930+2752 (Geier et al.

2007a).

The very similar HE 0929−0424 and

TONS 183 have to have quite massive com-

panions. Even in the less likely case that their

sdB primaries are of low mass (≈ 0.3 M ) the

companions would be heavy white dwarfs. At

the most probable sdB mass, however, their

companions would exceed the Chandrasekhar

mass limit. There are only two kinds of ob-

jects known with such high masses and such

low luminosities - neutron stars (NS) and stel-

lar mass black holes (BH). The two systems

HE 0532−4503 and PG 1232−136 have even

higher companion masses, which would ex- ceed the Chandrasekhar limit for any mass of a core helium-burning subdwarf star (see Fig. 1).

The three long period binaries HE 1448−0510, HE 2150−0238 and WD 0048−202 could not be solved with the described method. The min- imum sdB masses exceeded 1.3 M and were not consistent with the theoretical mass range.

These systems cannot be synchronized (see Sect. 5).

Binaries hosting a neutron star or a black hole are a very rare class of objects. From about 50 analysed sdB binaries in our samples, we found two, possibly four candidate systems.

This fraction of 4-8 % is much too high to be compatible with any binary evolution model known so far (Podsiadlowski priv. comm.).

Our results depend strongly on the pro- jected rotational velocity. The unexpectedly high masses could only be reduced if the v

sin i were underestimated. As described above we quantified all possible systematic ef- fects and the overall results were very con- sistent. But even if there would be unac- counted systematic effects (e.g. short period pulsations), they would always cause extra broadening of the lines. The measured broad- ening is then due to rotation plus the unac- counted effects, which means the deduced ro- tational broadening would be overestimated.

Potential systematic effects yet unaccounted for would therefore lead to even higher com- panion masses.

5. Orbital synchronization of sdB binaries

Our method rests on the assumption of orbital synchronization. We compared the v

sin i- distribution of close sdB binaries to the distri- bution of the single stars. A large fraction of binary sdBs exceeds the maximum v

sin i = 8.3 kms

, derived for the single sdB stars, sig- nificantly. The most likely reason for this is tidal interaction with the companion.

The question, which mechanisms are re- sponsible for the synchronization of such stars, is not yet settled. Subluminous B stars have convective cores and radiative en- velopes. The physical mechanisms for tidal

dissipation in such stars are under debate.

Different theoretical concepts (Zahn 1977;

Tassoul & Tassoul 1992) predict that the syn- chronization timescale t

depends strongly on the orbital period but differs in absolute val- ues. The sychronization times have to be lower than the average lifetime on the EHB of t

≈ 10

yr. Using the formalism of Zahn (1977) t

would exceed t

for periods longer than P

≈ 0.4 d, whereas this would be the case at P

≈ 2.0 d if we apply the theory of Tassoul & Tassoul (1992).

But as long as the question of tidal syn- chronization is not settled, all timescales have to be taken with caution. Detailed calcula- tions, which take the internal structure of sdBs into account, are not available and urgently needed. Observational constraints are neces- sary to guide the development of more sophis- ticated models.

Up to now such observational constraints are rare. Two short period (≈ 0.1 d) sdB bina- ries with white dwarf companions show light variations due to their ellipsoidal deforma- tion (Orosz & Wade 1999; Geier et al. 2007a) and are therefore most likely synchronized.

Geier et al. (2007b) verified that light varia- tions in the longer period (≈ 0.6 d) sdB+WD binary PG 0101+039 are due to ellipsoidal deformation and that tidal synchronization is most likely established. We conclude that this assumption should hold for all sdB binaries with orbital periods of less than half a day. Last but not least, van Grootel et al. (2008) carried out an asteroseismological analysis of the pul- sating sdB in the binary Feige 48 (sdB+WD, P = 0.376 d) and found it to be synchronized.

In Tab. 1 we show which ones of the bi- naries fullfill the empirical or theoretical crite- ria for synchronization. It is important to note that three of our candidate systems with mas- sive compact companions are consistent with all of them.

6. Conclusions

Out of 12 analysed sdB binaries, five have

companion masses compatible with white

dwarfs of typical masses or late type main se-

quence stars. The properties of these systems

Table 1. Orbital periods, inclination angles, companion masses and possible nature of the un- seen companions. The lower companion mass corresponds to an sdB of 0.3 M , the higher limit to an sdB of 0.48 M . Empirical indications for synchronization could be found in subdwarf binaries with longer periods by asteroseismological modelling

and/or detection of ellipsoidal deformation

. Theoretical synchronization timescales are shorter than the average EHB lifetime according to the theory of Zahn (1977)

and/or Tassoul & Tassoul (1992)

(see Sect. 5). Binaries up to orbital periods of 1.3 d can be solved consistently under the assumption of synchronization.

† Orbital period of this system taken from Napiwotzki et al. (2001).

System

Companion

[d] [deg] [M

]

HE 0532−4503

0.26560 ± 0.00010 13 − 17 1.40 − 3.60 NS/BH PG 1232−136

0.36300 ± 0.00030 14 − 19 2.00 − 7.00 NS/BH WD 0107−342

0.37500 ± 0.05000 37 − 50 0.48 − 0.87 WD HE 0929−0424

0.44000 ± 0.00020 23 − 29 0.60 − 2.40 WD/NS/BH HE 0230−4323

0.44300 ± 0.00050 38 − 50 0.18 − 0.35 WD/late MS TONS 183

0.82770 ± 0.00020 22 − 29 0.60 − 2.40 WD/NS/BH HE 2135−3749

0.92400 ± 0.00030 66 − 90 0.35 − 0.45 WD/late MS HE 1421−1206

1.18800 ± 0.00100 56 − 90 0.15 − 0.30 WD/late MS HE 1047−0436

1.21325 ± 0.00001† 62 − 90 0.35 − 0.60 WD/late MS

HE 2150−0238

1.32090 ± 0.00500 – – no solution

HE 1448−0510 7.15880 ± 0.01300 – – no solution

WD 0048−202 7.44360 ± 0.01500 – – no solution

are in full agreement with binary population synthesis simulations. Four binaries have sur- prisingly high companion masses, which leads to the conclusion, that the companions have to be white dwarfs of unusually high mass or even neutron stars or black holes. This high fraction cannot be explained by current evolu- tionary theory. As our analysis assumes syn- chronization a better understanding of this pro- cess for sdB stars is urgently needed. Three of our candidates pass all four criteria for syn- chronization, strengthening our conclusion. A larger sample of sdB binaries has to be stud- ied with our method to search for systematic trends and improve statistics. The presence of such a high fraction of heavy binaries in our samples raises several questions. Is the forma- tion and evolution of sdB stars linked to that of heavy compact objects like neutron stars or black holes? Can sdB stars be used as tracers to find more of these exotic objects? Is there a hidden population of these objects present in our galaxy?

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